I want to prove the following result: $$\int_0^1 \int_0^1 {f(xy)(1-x)^{p-1}y^p(1-y)^{q-1}} \mathrm{d}x \, \mathrm{d}y=\frac{\Gamma(p) \Gamma(q)}{\Gamma(p+q)} \int_0^1 {f(t)(1-t)^{p+q-1}} \mathrm{d}t.$$
I have tried using the substitution $t=xy$, but am not sure what to use for the other variable. We were given no information about the function $f$.
Any help would be appreciated!